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Optimal dividends and capital injection under dividend restrictions
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-0775-9680
Number of Authors: 22020 (English)In: Mathematical Methods of Operations Research, ISSN 1432-2994, E-ISSN 1432-5217, Vol. 92, p. 461-487Article in journal (Refereed) Published
Abstract [en]

We study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a givendividend payout barrierin order for dividend payments to be allowed. Bankruptcy occurs if the surplus process becomes negative and there are proportional costs for capital injection. We show that one of the following strategies is optimal: (i) Pay dividends and inject capital in order to reflect the surplus process at an upper barrier and at 0, implying bankruptcy never occurs. (ii) Pay dividends in order to reflect the surplus process at an upper barrier and never inject capital-corresponding to absorption at 0-implying bankruptcy occurs the first time the surplus reaches zero. We show that if the costs of capital injection arelow, then a sufficiently high dividend payout barrier will change the optimal strategy from type (i) (without bankruptcy) to type (ii) (with bankruptcy). Moreover, if the costs arehigh, then the optimal strategy is of type (ii) regardless of the dividend payout barrier. We also consider the possibility for the owner to choose a stopping time at which the insurance company is liquidated and the owner obtains a liquidation value. The uncontrolled surplus process is a Wiener process with drift.

Place, publisher, year, edition, pages
2020. Vol. 92, p. 461-487
Keywords [en]
Bankruptcy, Capital injection, Dividend restrictions, Insolvency, Issuance of equity, Optimal dividends, Reflection and absorption, Singular stochastic control, Solvency constraints
National Category
Economics and Business Mathematics
Identifiers
URN: urn:nbn:se:su:diva-185468DOI: 10.1007/s00186-020-00720-yISI: 000555568700001OAI: oai:DiVA.org:su-185468DiVA, id: diva2:1474885
Available from: 2020-10-10 Created: 2020-10-10 Last updated: 2022-02-25Bibliographically approved

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Lindensjö, KristofferLindskog, Filip

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